Your planet will either be incredibly cold, or have no heavy elements.
Krypton is a fairly light noble gas, it boils at 119K, and it's fairly rare. Naturally, such an element would never form the core of a planet. Even for planets where krypton occurs as a solid, heavier, denser materials will sink and form the core of the planet, especially when the planet is young and hot.
However, it would be possible to form a planet with a krypton core artificially, in one of two ways.
First, if your planet is incredibly cold, you could conceivably build a core of solid krypton, and then slowly add more materials to build up a planet on top of your core. If your planet is cold enough that nothing moves around, you'll end up with a krypton-cored planet. Your planet will be cold and inert, with no plate tectonics, earthquakes, or volcanoes. It will be far from its star. Superman might be able to live, there, but it wouldn't be much fun.
Second, you could have a planet where krypton is the densest material. Natural processes that can form Krypton can also form heavier elements, so this would never happen naturally. However, if your super advanced aliens were to strip all of the krypton out of a planet like Jupiter, and throw in some lighter elements to round out the planet, you could conceivably create a planet where krypton was the densest material available, and hence sank and formed the core. This would only happen if the planet were either gaseous, with the rest of the planet made of gasses less dense than krypton, or else if the planet was cold enough that the krypton solidified.
All of these planets could only be formed artificially, and none would support life.